From 18180491c228d018eef3eaea9fdc8fdce60adc09 Mon Sep 17 00:00:00 2001
From: felixm <mail@felixm.de>
Date: Fri, 6 Oct 2023 21:44:41 +0200
Subject: [PATCH] Solve first 70% problem 161.

---
 python/e111.py |   2 +-
 python/e161.py | 108 +++++++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 109 insertions(+), 1 deletion(-)
 create mode 100644 python/e161.py

diff --git a/python/e111.py b/python/e111.py
index 14137c2..dd3be37 100644
--- a/python/e111.py
+++ b/python/e111.py
@@ -35,7 +35,7 @@ def euler_111():
             for p in get_permutations(base, 2):
                 if is_prime(p):
                     subresult += p
-        assert subresult > 0, "More than to permutations required to yield prime"
+        assert subresult > 0, "More than two permutations required to yield prime"
         result += subresult
     return result
 
diff --git a/python/e161.py b/python/e161.py
new file mode 100644
index 0000000..591fed6
--- /dev/null
+++ b/python/e161.py
@@ -0,0 +1,108 @@
+from copy import copy
+from typing import Optional, Tuple
+
+
+CACHE = {}
+EMPTY = '⬛'
+FIELDS = ['🔴', '🟠', '🟡', '🟢', '🔵', '🟣', '⚪', '🟤', '⭐']
+
+
+# We use [row, col] indexing.
+BLOCKS = [
+    ((0, 0), (0, 1), (0, 2)), # dark blue
+    ((0, 0), (1, 0), (2, 0)), # black
+    ((0, 0), (0, 1), (1, 0)), # red
+    ((0, 0), (0, 1), (1, 1)), # green
+    ((0, 0), (1, 0), (1, 1)), # blue
+    ((0, 0), (1, 0), (1, -1)), # orange
+]
+
+
+class Field:
+
+    def __init__(self, N_COLS, N_ROWS):
+        self.N_COLS = N_COLS
+        self.N_ROWS = N_ROWS
+        self.state = 0
+
+    def __hash__(self):
+        return hash(self.state)
+
+    def get_first_empty(self) -> Optional[Tuple[int, int]]:
+        for row in range(self.N_ROWS):
+            for col in range(self.N_COLS):
+                if self.is_empty(row, col):
+                    return (row, col)
+        return None
+
+    def is_empty(self, row: int, col: int) -> bool:
+        index = row * self.N_COLS + col
+        result = not bool(self.state & (1 << index))
+        return result
+
+    def set(self, row: int, col: int):
+        index = row * self.N_COLS + col
+        self.state |= (1 << index)
+
+    def __getitem__(self, row: int):
+        return [self.is_empty(row, col) for col in range(self.N_COLS)]
+
+    def print(self):
+        for row in range(self.N_ROWS):
+            row_str = ""
+            for col in range(self.N_COLS):
+                row_str += '⬛' if self.is_empty(row, col) else '⚪'
+            print(row_str)
+
+
+def fits(field, block, coord):
+    N_ROWS = field.N_ROWS
+    N_COLS = field.N_COLS
+
+    for rel_coord in block:
+        abs_row = coord[0] + rel_coord[0]
+        abs_col = coord[1] + rel_coord[1]
+
+        if abs_row < 0 or abs_col < 0 or abs_row >= N_ROWS or abs_col >= N_COLS:
+            return None
+
+        if not field.is_empty(abs_row, abs_col):
+            return None
+
+    new_field = copy(field)
+    for rel_coord in block:
+        abs_row = coord[0] + rel_coord[0]
+        abs_col = coord[1] + rel_coord[1]
+        new_field.set(abs_row, abs_col)
+
+    return new_field
+
+
+def count(field):
+    global CACHE
+
+    if hash(field) in CACHE:
+        return CACHE[hash(field)]
+
+    first_empty = field.get_first_empty()
+    if first_empty is None:
+        return 1
+    
+    result = 0
+    for block in BLOCKS:
+        if (new_field := fits(field, block, first_empty)) is not None:
+            result += count(new_field)
+
+    CACHE[hash(field)] = result
+    return result
+
+
+def euler_161():
+    return count(Field(9, 12))
+
+
+if __name__ == "__main__":
+    solution = euler_161()
+    print("e161.py: " + str(solution))
+    assert(solution == 20574308184277971)
+